US2025068395A1PendingUtilityA1
Inner Products with Secure Multi-Party Computations
Est. expiryFeb 28, 2042(~15.6 yrs left)· nominal 20-yr term from priority
Inventors:Miguel De Vega Rodrigo
H04L 2209/04H04L 2209/46G06F 7/582H04L 9/0894
29
PatentIndex Score
0
Cited by
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Claims
Abstract
A secure multiparty computation method permits the computation of an inner product of a pair of secret vectors. The vectors are transformed and blinded using various blinding factors with the transforms of the vectors being according to a discrete linear transform for which Parseval's theorem holds. Shares of the transformed, blinded vectors are distributed to computing nodes which each calculate shares of a result without access to the secrets, and the result shares can be combined to generate the inner product of the original vectors.
Claims
exact text as granted — not AI-modified1 . A method of performing a multi-party computation by a network of data processors, said data processors comprising first and second dealer nodes, a plurality of M computing nodes, and at least one result node, the method comprising:
(a) providing the first dealer node with a random vector A having components (A 0 , A 1 , . . . , A M−1 ) all of which are non-zero; (b) providing the second dealer node with an inverse vector A −1 having components (A 0 −1 , A 1 −1 , . . . , A M−1 −1 ), such that for each i∈{0, . . . , M−1}, the product A i ·A i −1 =1; (c) the first dealer node computing a first transformed vector X=(X 0 , X 1 , . . . , X M−1 ) of a first private input vector x=(x 0 , x 1 , . . . , x M−1 ), according to a discrete linear transform for which Parseval's theorem holds; (d) the first dealer node computing a first blinded vector U=(U 0 , U 1 , . . . , U M−1 ) as U=A∘X where the operator ∘ represents the Hadamard product; (e) the second dealer node computing a second transformed vector Y=(Y 0 , Y 1 , . . . , Y M−1 ) of a second private input vector y=(y 0 , y 1 , . . . , y M−1 ), according to said discrete linear transform; (f) the second dealer node computing a second blinded vector V=(V 0 , V 1 , . . . , V M−1 ) as V=A −1 ∘Y where the operator ∘ represents the Hadamard product; (g) the first dealer sending the i-th component U i of the first blinded vector U to the i-th computing node for each i∈{0, . . . , M−1}; (h) the second dealer sending the i-th component V i of the second blinded vector V to the i-th computing node for each i∈{0, . . . , M−1}; (i) for each j∈{0, . . . , (M−1)}, the j-th computing node:
calculating from its received components U j and V j a result share
R
j
=
1
M
U
j
·
V
j
,
and
sending the result share R j to one or more of the one or more result nodes;
(j) said one or more result nodes calculating, from the M received result shares R j for j∈{0, . . . , M−1}, the inner product of the first and second private input vectors x, y as:
〈
x
,
y
〉
=
∑
j
=
0
M
-
1
R
j
2 . The method according to claim 1 , wherein the first and second dealer nodes generate the first and second private input vectors x and y of dimension M, respectively, as expansions of original unexpanded private input vectors x orig and y orig of dimension N, respectively, where N<M, and where:
x
orig
=
(
x
0
,
x
1
,
…
,
x
N
-
1
)
y
orig
=
(
y
0
,
y
1
,
…
,
y
N
-
1
)
x
=
(
x
0
,
x
1
,
…
,
x
N
-
1
,
x
N
,
…
,
x
M
-
1
)
y
=
(
y
0
,
y
1
,
…
,
y
N
-
1
,
y
N
,
…
,
y
M
-
1
)
and where the components x N , . . . , x M−1 and y N , . . . , y M−1 are chosen such that:
∑
i
=
N
M
-
1
x
i
·
y
i
=
0
3 . The method according to claim 1 , wherein the steps of providing the first and second dealers with the random vectors A and A −1 comprise both dealers operating a pseudo-random number generator in sync to generate the components of vector A, and the second dealer node calculating A −1 from the vector A.
4 . The method according to claim 1 , wherein the steps of providing the first and second dealers with the random vectors A and A −1 comprise a trusted third party node communicating vector A to the first dealer node and either vector A or vector A −1 to the second dealer node.
5 . The method according to claim 1 , wherein the steps of providing the first and second dealers with the random vectors A and A −1 comprise communicating either vector A or vector A −1 cryptographically to at least one of the first and second dealer nodes.
6 . The method according to claim 1 , wherein the vector A is {1, 1, . . . , 1}.
7 . The method according to claim 1 , wherein the private input vectors have integer components and arithmetical operations are performed modulo a prime number p.
8 . The method according to claim 1 , wherein the discrete linear transform for which Parseval's theorem holds is selected from:
the Number Theoretic Transform (NTT); the Fermat Number Transform (FNT); the Mersenne Number Transform (MNT); the Discrete Fourier Transform; the Z-Transform; the Discrete Hartley Transform; the Discrete Wavelet Transform with arbitrary orthogonal wavelet bases, such as Haar, Daubechies, Simlets, Coiflets, Meyer, Morlet and Gaussian wavelet families.
9 . The method according to claim 1 , wherein the discrete linear transform is not the null function.
10 . The method according to claim 1 , wherein the discrete linear transform is not the identity function.
11 . The method according to claim 1 , wherein the private input vectors have real or complex number components.Join the waitlist — get patent alerts
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